The strong geometric lemma holds for Lipschitz graphs in \(\mathbb {R}^n\)  by a result of Dorronsoro, obtained in [1]}, and is one of the foundations of uniform rectifiability in \(\mathbb {R}^n\) . In particular, an Ahlfors regular subset of \(\mathbb {R}^n\)  satisfies a Euclidean analogue of (REF ), with constants depending only on \(n\)  and the Ahlfors regularity constant of the set, if and only if it is uniformly rectifiable, see [2]}.
